You have 6 hex characters.

The first has 16 possible values;

The second also has 16 possible values for each of those 16, so now we have 16 times 16.

etc.

So it's a choice from 16, repeated for a total of 6 times.

That's 16 times 16 times ... times 16, which is 16^6.

Welp, you got me scrolling your HN thread to see where the "two-trillion-something" number came from. Between this and your experiment site, you have a knack for drawing attention.

If you think 3 positions, each 0-1, gives 3^2 options, then please show us the 9th three-bit number. Even simpler is the case of 1 position that is 0-1. Does that give 1^2 or 2^1 options?

1 byte (8 bits) is 2^8 (256 unique combinations of bits)

3 bytes (24 bits) is 2^24 (16777216 unique combinations of bits)

256^3 == (16^2)^3 == 16^(3*2) == 16^6

Yes.

16^6 is not 6^16.

Yes, each possible 6^16 outcome is it's own subpage...

/000000 /000001 /000002 /000003 etc...

Or am I missing something?

You are missing something. How many two-digit decimal numbers are there from 00 to 99? Obviously 99+1 = 100: 10 options for the first digit times 10 options for the second digit; 10 in the form 0X, 10 in the form 1X, etc. up to 9X, a total of 10 * 10 = 10^2.

So how many 6-digit hexadecimal numbers from 0x000000 to 0xffffff? 0xffffff+1 = 16777216 = 16^6. 16 options for the first digit, times 16 options for the second digit, times 16 for the 3rd, times 16 for the 4th, times 16 for the 5th, times 16 for the 6th is 16^6. Or go to bytes: 3 bytes, each with 256 possible values is 256^3 = (16^2)^3 = 16^6. Or bits: 2^24 = (2^4)^6 = 16^6.

It's also pretty trivial to just count them. Run this in your browser console:

  count = 0; for(i = 0x000000; i <= 0xffffff; i++) { count++; } console.log(count, 16**6, 0xffffff+1, 6**16)

16^6 == 256^3 == 2^24 == 16,777,216

You have it backward. There are 16^6 URLs, not 6^16.

you mean 16^6